Forward Period Analysis Method of the Periodic Hamiltonian System

Using the forward period analysis FPA, we obtain the period of a Morse oscillator and mathematical pendulum system, with the accuracy of 100 significant digits. From these results, the long-term 0, 1060 time unit solutions, ranging from the Planck time to the age of the universe, are computed reliably and quickly with a parallel multiple-precision Taylor series PMT scheme. The application of FPA to periodic systems can greatly reduce the computation time of long-term reliable simulations. This scheme provides an efficient way to generate reference solutions, against which long-term simulations using other schemes can be tested.